A new factorization technique using quadratic forms

Authors:
D. H. Lehmer and Emma Lehmer

Journal:
Math. Comp. **28** (1974), 625-635

MSC:
Primary 10A25; Secondary 10-04, 10B05

DOI:
https://doi.org/10.1090/S0025-5718-1974-0342458-5

MathSciNet review:
0342458

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Abstract | References | Similar Articles | Additional Information

Abstract: The paper presents a practical method for factoring an arbitrary *N* by representing *N* or by one of at most three quadratic forms: . These three forms appropriate to *N*, together with inequalities for *y*, are given for all *N* prime to 6. Presently available sieving facilities make the method quite effective and economical for numbers *N* having 20 to 25 digits. Four examples arising from aliquot series are discussed in detail.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1974-0342458-5

Keywords:
Factorization,
primality,
binary quadratic forms,
representation

Article copyright:
© Copyright 1974
American Mathematical Society